Selfdischarge and leakage current
The selfdischarge is an important parameter for the applications in which the supercapacitors are not connected to an electrical network which could maintain its state of charge. In those applications the device is supposed to be able to deliver power with a performance not deteriorated by the rest time. A typical example is the cranking of a car engine after a week spent at rest in an airport parking lot. In this case, it's necessary that the storage device maintains its tension as high as possible because the available power and the stored energy decline with the square of this tension.
The voltage drop with the time of a charged capacitor in a floating mode may be due to different discharging mechanisms, which are:
- the leakage current,
- the charge redistribution
The charge redistribution corresponds to the displacement of charges from an easy access charged area of the electrode with a low access time constant, to a more difficult one, with a higher time constant. The charge redistribution, contrarily to the selfdischarge, may lead to a voltage increase measured at the capacitor terminal. After a fast capacitor discharge, the voltage may increase a little bit due to the arrival of charges of slow areas. The leakage current may be due to redox reactions, ionic charge diffusion or/and electronic partial discharge through the separator. The selfdischarge amplitude is determined, either by measuring the current necessary to feed to keep a constant voltage (in the microamperes range), or by recording the capacitor voltage as a function of the time.
The diagnostic can be performed according to the voltagetime dependency. If the voltage drops with an unwanted logarithmic law, U(t) vs. log t (see fig. 1), the mechanisms are controlled by Faradic self-discharge from overcharge or from impurities redox reactions.
If the voltage drops with a square root function of the time, U(t) vs. t (see fig. 2), the mechanisms are controlled by diffusion.
These dependencies may be demonstrated with the representation of the selfdischarge behavior of different capacitors. BCAP0007 and BCAP0008 are Maxwell commercial products with only a diffusion driven selfdischarge mechanism, while BCAPproto is a prototype with a very high impurity content which is submitted to redox reactions. The two different plots show the respective linear drop in the respective representations.
Recent measurements have shown that 10 years are necessary to fully discharge a supercapacitor of the new generation at room temperature.
The supercapacitor selfdischarge performance is the result of a compromise with its power capability. The manufacturers could use a thicker separator to improve the voltage retention but this operation would increase in the same time the series ionic resistance.
An other way of characterizing the selfdischarge of a supercapacitor is to measure the leakage current. In the following graph the leakage current of 350 Farad cell has been measured for different temperatures and for different voltages. The leakage current increases both with the temperature and the voltage . In a first approximation both reactions will follow the ButlerVolmer behavior and therefore the slope of the lines can be called an effective Tafel slope. The effective Tafel slope for the leakage current is about 0.4V at 20 °C. At 60 °C the Tafel slope increases to 0.6V. This behavior is very important for the considerations which must be done for determining the cell balancing strategy used in the supercapacitor module.
R. Kötz, et al., Journal of Power Sources 174 (2007) 264271, "Voltage balancing: Long term experience with the 250V supercapacitor module of the hybrid fuel cell vehicle HY-LIGHT (Michelin +PSI)